You need to override some files in your custom plugin:

\views\default\object\comment.php
\views\default\object\elements\full.php
\views\default\object\elements\full\header.php
\views\default\object\elements\summary.php
\views\default\object\elements\summary\metadata.php

Edit \mod\your_plugin\views\default\object\comment.php to provide the new views:

\mod\your_plugin\views\default\object\comment\elements\full.php
\mod\your_plugin\views\default\object\comment\elements\summary.php

Edit these new views to provide another new views:

\mod\your_plugin\views\default\object\comment\elements\full\header.php
\mod\your_plugin\views\default\object\comment\elements\summary\metadata.php

Your goal is to extract elgg_view_menu('social') from

\mod\your_plugin\views\default\object\comment\elements\summary\metadata.php

and place it in a new view, e.g.

\mod\your_plugin\views\default\object\comment\elements\summary\social.php

Then you can place this social.php view to \mod\your_plugin\views\default\object\comment.php under $params['content'] for:

echo elgg_view('object/comment/elements/full', $params);

and

echo elgg_view('object/comment/elements/summary', $params);

Some CSS magic then and done ;)

Thanks for the help. It worked :)